Biology Forums - Study Force

(Note- these are not inequalities)

The question, straight from my sheet:

"Graph the absolute value functions listed below. For each, state the domain and the range."

Now, to graph them all I did was make an x|y chart. That wasn't too dificult. But I don't know how I state the domain and the range. Here's an example of one of the equation: y=|x-3|

Can someone show me how to figure out what the domain and the range are, and tell me how to figure them out just by looking at the graph? Thank you!

Well, if you look at your graph, you should see that the domain is all real numbers, because x extends infinitely in both directions. You can tell this by looking at the equation, too, because there is no value of x that is not possible in the equation. However, there is a restriction on the range, because y has a minimum value. If you look at your graph, it's easy to see that the lowest y-value is 0, and you can tell this from the equation because absolute value is always greater than or equal to 0.

Therefore:
Domain: R
Range: y is greater than or equal to 0.

The domain is all real numbers.
x  |x-3|
-4 7
-3 6
-2 5
0 3
1 2
2 1
3 0
4 1
etc.
The range is all positive real numbers and 0.
Domain : (-?,?)
Range : [0, ?)

You should know that the graph of y = |x| is a V-shaped graph which is symmetric to the y-axis and is always positive. The two llines forming the V originate at the origin (0,0) and go at 45 degree angles (one with a slope of 1 and one with a slope of -1).

Thus x can have any real value so its domain is all the real numbers. Since y is always >= 0 its range is from 0 to infinity.

Now the graph of y = |x-3| is the same as that of y = |x| except it is moved horizontally 3 units to the right. Hence domain and range of y = |x-3| are same as for y = |x|.

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